Hydrodynamics of local excitations after an interaction quench in 1<i>D</i>cold atomic gases
Abstract
We discuss the hydrodynamic approach to the study of the time evolution -induced by a quench- of local excitations in one dimension. We focus on \ninteraction quenches: the considered protocol consists in creating a stable \nlocalized excitation propagating through the system, and then operating a \nsudden change of the interaction between the particles. To highlight the effect of the quench, we take the initial excitation to be a soliton. The quench \nsplits the excitation into two packets moving in opposite directions, whose \ncharacteristics can be expressed in a universal way. Our treatment allows to \ndescribe the internal dynamics of these two packets in terms of the different \nvelocities of their components. We confirm our analytical predictions through \nnumerical simulations performed with the Gross-Pitaevskii equation and with the Calogero model (as an example of long range interactions and solvable with a parabolic confinement). Through the Calogero model we also discuss the effect of an external trapping on the protocol. The hydrodynamic approach shows that there is a difference between the bulk velocities of the propagating packets and the velocities of their peaks: it is possible to discriminate the two quantities, as we show through the comparison between numerical simulations and analytical estimates. In the realizations of the discussed quench protocol in a cold atom experiment, these different velocities are accessible through different measurement procedures.